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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

SKILLS Plus

Family of Ellipses

(a) Use a graphing device to sketch the top half (the portion in the first and second quadrants) of the family of ellipses x 2 + k y 2 = 100 for k = 4 , 10 , 25, and 50 .

(b) What do the members of this family of ellipses have in common? How do they differ?

To determine

(a)

To graph:

The top half of the family of ellipses x2+ky2=100 for k=4, 10, 25, and 50.

Explanation

Calculation:

The equation for the family of ellipses x2+ky2=100 for k=4, 10, 25, and 50 is given by,

For k=4, the equation of ellipse is x2100+y225=1.

Solve for y,

x2100+y225=1y2=25(1x2100)y=±5(1x2100)

The top half of the ellipse is given by y=+5(1x2100).

For k=10, the equation of ellipse is x2100+y210=1.

Solve for y,

x2100+y210=1y2=10(1x2100)y=±10(1x2100)

The top half of ellipse is given by y=+10(1x2100).

For k=25, the equation of ellipse is x2100+y24=1

To determine

(b)

To find:

The common value in the family of ellipses x2+ky2=100 for k=4, 10, 25, and 50.

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